Ty Aderhold and David Freed are second-year members of the Harvard Sports Analysis Collective. Ty is a sophomore majoring in History and Science with a minor in Global Health and Health Policy, and is a big fan of all Atlanta sports teams (proving Atlanta sports fans do actually exist). David is majoring in applied math (focusing on economics) and minoring in statistics. He is currently looking for a vintage Vince Carter Raptors jersey.

One of the biggest stories from Sunday was Calvin Johnson’s monstrous 329-yard receiving day, which prompted teammate Reggie Bush to call him “the greatest of all time” after the game. By contrast, because it came in a win, Tom Brady’s 116-yard performance went under the radar. Johnson’s big day and Brady’s less-than-stellar one prompt questions about the relationship between a quarterback and his top receiver.

One of the central figures in this debate is Matthew Stafford. For almost his entire NFL career, many have considered him a quarterback that relies on Johnson for his success. Stafford’s recent struggles in the Lions’ Week 5 game against the Packers in which Johnson didn’t play only added credence to this theory. At the same time, Tom Brady has been regarded for years as a superstar quarterback that can generate above average stats for otherwise pedestrian receivers. Many considered it to be Brady that made Wes Welker great, not the other way around. However, it has been apparent throughout the season, as it was against the Dolphins this past weekend, that Brady is suffering from a lack of talented receivers (and, potentially, an undisclosed injury). This post takes a step towards separating the value of a quarterback from his top receiver so we can better compare quarterback play across the league. It will also take an in-depth look at Matthew Stafford and Tom Brady with the goal of better understanding these quarterbacks and their successes with the likes of Calvin Johnson and Wes Welker.

To begin separating out the value of a quarterback from that of his top receiver, we looked at the best quarterback from each team in 2012 and his top receiver (defined as the receiver who gained the most yards). We also limited our data only to games that the quarterback and receiver played together. After computing the raw quarterback ratings for each quarterback, we subtracted those plays on which he targeted his best receiver and recalculated his statistics.

As we can see above, quarterbacks on the whole tended to throw slightly worse to their secondary and tertiary targets with a couple exceptions. Most notably, Ben Roethlisberger went from the eighth in quarterback rating to the second-rated quarterback because of the low completion percentage and five interceptions he threw when targeting Mike Wallace. On the flip side of the coin, Peyton Manning was nearly perfect throwing to Demaryius Thomas in 2012 (11 touchdowns, no picks) but not as spectacular throwing to Eric Decker, Jacob Tamme, and co. (26 touchdowns, 11 picks). Likewise, Colin Kaepernick (-27 change in QB rating) and Jay Cutler (-10) had drastic drops in production when defenses closed off Michael Crabtree and Brandon Marshall, respectively.

Across the board, quarterbacks suffered an average decrease of 3.1 points in QB rating when they did not throw to their favorite targets. Only five quarterbacks improved their score, none more than John Skelton, who managed to completed only 43% of his passes to Larry Fitzgerald while throwing in four picks.

One of those who fell? The much-maligned Stafford, whose QB rating fell 3.6 points without Calvin Johnson to throw to. Considering that a little less than 40 percent of Stafford’s yards went to Johnson and he threw to him on 27.3 percent of plays, the Georgia product’s dependence on Megatron shows up early and often. Days like Sunday, where only 16 of Stafford’s 48 throws go to Megatron but account for 329 of Stafford’s 488 yards further substantiate the idea that Stafford is a product of Megatron. Digging deep into the data appears to validate, at least in part, this argument.

Here we can actually see, contrary to the main argument, that Stafford is as good or worse completing passes to Johnson as he is the rest of his wide receiving core. Because Johnson frequently draws double coverage—Stafford completed 14 of his 16 pass attempts to Megatron on Sunday when Dallas put one man on him all day—this is not surprising, even for a man capable of catches like this.

Here we can see both the argument for Stafford’s development this year and the main reason detractors think Megatron makes Stafford a better player. In 2011, Stafford’s best year to date, nearly half of his touchdowns went to Johnson. The gap was smaller last year because Johnson caught only five touchdowns (against five picks thrown in his direction), and this year Stafford has been only a hair (0.1 QB rating points to be exact) different throwing to Johnson versus his other receivers.

Here is the strongest argument for Stafford’s reliance on Johnson. When throwing to Johnson, Stafford is in the elite range in the NFL. When you take him away, he becomes, well, Christian Ponder. And that might be generous. Stafford qualified 21st in the NFL last year in yards per attempt, but on throws that he didn’t target Megatron, his 5.7 mark would have been worst in the league. That’s 0.3 worse than Blaine Gabbert and only 0.6 better than what Josh Freeman has put up this season.

The case against him is better when you consider the unusual circumstances surrounding the QB rating algorithm. Over the last two years, Stafford has thrown only 12 touchdowns to Johnson while throwing nine picks in his direction. By comparison, the Stafford-to-Johnson connection produced 18 touchdowns and four picks in 2011. The difference? Last year, Calvin Johnson was tackled eight times inside the five yard line—the second highest total of any receiver in the 2008-2012 seasons. If Johnson gets into the end zone a couple more times, the QB rating discrepancy in 2012 would match that of 2011.

However, while Stafford has been criticized for the success of his best receiver, this year Tom Brady has been given a free pass for poor performance (his QBR of 48.6 currently ranks 17th in the NFL) for losing all of his favorite targets.

Tom Brady’s QB rating fell by 2.3 when he wasn’t throwing to his top receiver in 2012, Wes Welker. While this is lower than the average for 2012, looking at Brady’s last five years shows that he fluctuated between a drop-off of 6.4 in 2009 to an increase of 0.3 in 2010 when not throwing to his first target. This year has seen a significant drop-off in QB rating for Brady that coincides with the loss of his top target over the four previous years. Here is the graph of the change in QB rating when not throwing to his top target:

This graph hints at the idea that Brady may actually depend on his receivers just as much as many other quarterbacks. Consider the case of 2009, when even with Randy Moss terrorizing the league, Welker was still Brady’s top target, and Brady had a much higher QB rating when throwing to Welker than to the rest of his still dominant receivers. 2011 also serves as another example of this since Brady’s QB rating dropped when he wasn’t targeting Welker, even though he had the likes of Rob Gronkowski and Aaron Hernandez as second and third options.

Though this idea might seem like a knock on Brady, it actually lends support to the idea that the reason he has struggled so mightily this season is due to a lack of receivers more so than a decline in talent.

As you can see, it is not just the loss of Welker that is affecting Brady. Gronkowski and Hernandez were Brady’s third and fourth targets according to yards in 2012, and their absence this year has been part of the huge drop in Brady’s overall QB rating. Current third and fourth receivers Aaron Dobson and Danny Amendola have been a collection of drops and injuries all year; as the chart shows, a healthy Gronkowski was Brady’s best target last year and his return may signal an upswing this year. While this chart alone does not prove that Brady is not in decline, it does help illustrate his struggles this year are at least in part due to a sharp decline in his receiving corps.

Ultimately, the naysayers on Brady and Stafford both have strong evidence to point to. Stafford’s YPA numbers when he isn’t throwing to Megatron are at or near the bottom of the league; likewise, Brady has had trouble with his tertiary targets after losing the receiving depth he had last year. However, the data is not yet clear. So far this year, Stafford has been much better throwing to secondary targets—the strike to Kris Durham on the final drive as a good example—with a nearly equal QB rating to and away from Johnson. Likewise, at 36, Brady is already on the downward side of the aging curve, and his rating throwing to his top target dropped nearly fifteen points since last year.

In the bigger picture, this is a first step towards isolating the contributions of receivers from their quarterbacks. Such a task is made much more complicated for the two interdependent positions by the fact quarterbacks and receivers rarely (if ever) take the field without the other. Even on plays where Stafford does not target Johnson, Megatron’s ability to capture double coverage necessarily draws another defender off the quarterback’s other targets. This effect inflates the statistics of quarterbacks targeting their secondary receivers, so our results should not be interpreted as the true skill level of the quarterback without his top receiver, but rather his efficiency when not targeting his primary receivers. There is more to be done, but the first steps should give both detractors and fans of Stafford and Brady ammunition in the argument about their quarterback’s NFL worth.

13 Responses to “Separating Receiver from Quarterback: A Start”

only way to separate a receiver from a QB is to drag him off. This article is missing one thing: quotes for expert Football people. There's a whole lotta words up there but not one of them from somebody who played that game like me and such. This site needs more of these: " " and less of theses:+=

On any given Sunday you've got to go big or go home because if you don't leave it all on the field then it is what it is.

I think the pertinent point is in the last paragraph. Certainly Calvin Johnson has an impact on Stafford's effectiveness even when he's not throwing to him by drawing away coverage. There Stafford throwing to anyone (incl. Johnson) with Johnson on the field, Stafford throwing to Johnson, Stafford throwing to other receivers with Johnson on the field, and then Stafford throwing to other receivers WITHOUT Johnson on the field. Seems like you'd need to understand all these to truly understand WR impact.

Finally, at the risk of slightly agreeing with John Black . . . scheme matters as well, Johnson is often running deep routes and Stafford with his arm but so-so accuracy may be relatively more effective on those types of routes than other QB's. Throwing to other receivers with Johnson on the field, therefore, may be playing to his weaknesses . . . but if Johnson were injured, another wideout may run those deep routes emphasizing his strrengths, aso the drop-off may not be as big as one would expect based on the Johnson-target/Johnson-non-target analysis.

Not sure what the point really is here. Throwing to CJ is obviously a brilliant tactical move, because he is a great player. Of course results should be better with him. Keep in mind the "non-CJ" receivers were patrick edwards (not in nfl anymore), Durham (draft bust), ogletree (cut by dallas), etc. These wrs are bums. in fact, tom brady has better wrs than the lions do (outside of CJ).

One linguistic gripe: a group of receivers is a CORPS, not a CORE. One is from the Latin for "body" and means a group; the other is from the Latin for "heart" and refers to something central. Whoever does proofing/editing for this site usually avoids that kind of mistake.

Great article HSAC. I think this is most valuable as a comparison between quarterbacks, but also could be used to predict dropoff if a receiver is no longer playing (injury/trade, etc). Mike Wallace to the fins is an example of this.

That being said, I'd like to see this using EPA/P or Success Rate instead of QBR.

It says that Stafford drops off significantly when not throwing to Johnson, but almost every QB does poorly without his top target, especially if you consider the quality of Stafford's other receivers.

Where's the discussion of Nash equilibria regarding throwing to vs. throwing away from your top receiver??

In theory a quarterback should be just as good throwing to his best receiver as throwing to his worst, if he is mixing his strategy properly. The only way to control for the contribution of one or the other would be to look at their performance separate from one another, and there is obviously a terribly small sample size for that in most cases.

Tom Brady's receivers (Moss, Welker Stalworth) helped a backup who hadn't started a game since high school to a 104 EPA season, 63% completion rate, and $62 million contract -- after which he's had a career -22 EPA and never gotten his completion % above the 50s% ... so I imagine those receivers helped Tom's numbers too.

I've been annoying people here and elsewhere for years by saying a QB's stats reflect the rest of the team's performance at least as much, often more, than they do his own. (Say "Earl Morral", twice.)

Lombardi said the QB is the linch-pin of the offense whose job it is to get all the other players on offense to contribute at their best level -- and thus, a bad QB who fails to do that can destroy an offense all by himself (with picks, dumb sacks, mis-reads, etc), while a top QB can rise only to the level of the offensive talent as a whole, of which he is only 1/11th.

Just a thought. I think there may be a bit of flawed logic in considering the WR who gained the most yards as the QB's "best receiver". Let me demonstrate my belief to you through a hypothetical example.

Let's say WR #1 had 60 receptions and compiled 1,000 receiving yards. Now let's say that WR #2 had 80 receptions but compiled only 950 receiving yards. Does that imply that WR #1 is the better receiver? Certainly not. In fact, I think most would argue that WR #2 is the better receiver because he caught more balls.

Obviously there are more traits that determine which WR on a team is the "best", but unfortunately there is no clear-cut way of determining which one it is. In my example, you could make an argument that either WR is the best, but until there is a way to objectively state which WR is better, I'm afraid this study's findings skewed by subjectivity.

Great overall concept but, as with any advanced study of NFL stats, the findings are a bit muddy due to lurking variables.

to Zachary Beards point, I would also say that there is the problem of circularity here in that IF the number on receiver is the best, then by defn, a completion (at least virtually always) be contribute to a HIGHER QB rating. i.e, imagine a player catches balls for 4000 yards. what is the QB rating going to be on attempts to that player? quite high.

to Jim Glass, you make great point about Earl Morrall and Matt Cassell, but I would throw out the name of Peyton Manning, and the Colts going 2-14 without him. also, regarding the quote about Lombardi, he said it in an era where a QB was closer to being 1/11 of the offense.

The reason Stafford's YPA drops off so far when Megatron isn't in the occasion should be blatantly obvious when you look at the main passing options he has NOT named Calvin Johnson.

His WR corps is worse than mediocre and the primary receiving options are a pair of 2 dimensional RBs who are good in the receiver game (Bell and Bush) and Pettigrew... you're not going to stretch the field with that when 2 of your next best targets are coming out of the backfield.

@BBurkeESPN

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